What is the measure of the largest angle of triangle ABC if BC=9 , AC=10 and AB=13 ?
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Since the lengths of the 3 sides are given, we'll use the law of cosines to determine the measure of the largest angle.
The largest angle is the opposite angle to the largest length of triangle. Since the length of AB is the largest, then the measure of the angle C has to be determined.
cos C = (BC^2 + AC^2 - AB^2)/2BC*AC
We'll replace the sides by its lengths:
cos C = (81 + 100 - 169)/180
cos C = 12/180
cos C = 1/15
cos C = 0.067
C = 86.2 degrees
The measure of the largest angle of triangle ABC is: C = 86.2 degrees.
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